A student lost $\frac{2}{5}$ of his money during the break time, but then found $\frac{3}{4}$ of the amount lost. If he now has N 252, how much was his original money?
Answer (2)
Let x be the original amount of money.
The student lost 5 2 x and found 4 3 × 5 2 x = 10 3 x .
Set up the equation: x − 5 2 x + 10 3 x = 252 .
Solve for x : x = 9 2520 = 280 . The original amount of money was 280 .
Explanation
Problem Analysis Let's analyze the problem. The student lost a fraction of his money and then found a fraction of what he lost. We need to find the original amount of money he had, given the final amount.
Defining Variables and Lost/Found Amounts Let x be the original amount of money the student had. The student lost 5 2 of his money, which is 5 2 x . Then, he found 4 3 of the amount he lost. The amount he found is 4 3 × 5 2 x = 10 3 x .
Setting up the Equation The amount of money the student has now is the original amount minus the amount lost plus the amount found: x − 5 2 x + 10 3 x . We are given that the student now has N 252, so we can set up the equation: x − 5 2 x + 10 3 x = 252 .
Solving for x Now, let's solve the equation for x . First, we find a common denominator, which is 10. So, we rewrite the equation as: 10 10 x − 10 4 x + 10 3 x = 252 . Combining the terms, we get: 10 10 x − 4 x + 3 x = 252 , which simplifies to 10 9 x = 252 .
Isolating x To solve for x , we multiply both sides of the equation by 10: 9 x = 2520 . Then, we divide both sides by 9: x = 9 2520 .
Final Calculation Calculating the value of x , we get x = 280 . Therefore, the original amount of money the student had was N 280.
Conclusion The original amount of money the student had was N 280.
Examples
This problem demonstrates how to track gains and losses, which is a fundamental concept in personal finance. For example, if you invest N 1000 in the stock market and lose 20% of your investment, you would have N 800 left. If you then recover 15% of your initial investment, you would have N 950. Understanding these calculations helps you manage your finances effectively and make informed decisions about investments and savings.
The original amount of money the student had was N280 after losing 5 2 of his money and then finding 4 3 of the amount lost. We set up an equation to combine these amounts and solve for the original total. Thus, the original money is N280.
;
